The wealthy tend to have more wealth invested in the stock market. Most middle class wealth is invested in real estate, specifically the house they are living in.
While this is true for many, the extent of 401(k) might signal differently. Also, most of the wealthy I know have far less in the stock market than you might imagine. Real Estate, development and private placements. Stock Market is too tax inefficient.
Keep in mind that when referring to real estate the value is often the equity (asset - debt) not the asset value itself. Pretty sure that is the case with SCF data from the Census.